Use negligent when you want to describe someone who just doesn't give a hoot. You can be negligent at work if you let the work pile up while you play computer games, or you can be negligent at home if you haven't fed your fish for six days straight.
The adjective negligent comes from the Latin word Camera Across Ralph Bag Body Merlot Small Saffiano Lauren neglegentia, meaning "carelessness." Other words that share the same roots include the noun negligence and neglect — which has both noun and verb forms. All three words have meanings that imply the same sort of thing — a lack of attention to the well being of something or someone.